You will receive a random Attribute Power and a Bonus Effect on your first reincarnation, they will only change with Soul Stoneand Soul Refining Stone (explained on Changing Bonus section of this thread), also to be given randomly, you can get this by finishing all stages of Conquest Of Might - Soul Society (Lv.70) also on Sign in Rewards and Bleach Events.

Not Reincarnated
- Do 30% less damage in PVE and PVP, get 30% back in PVE by reincarnating your main and partners.
- All reincarnated will do atleast a minimum of 16% to none reincarnated.
- PVE and PVP(NonReincarnated Vs NonReincarnated) should NOT be affected by these, Reincarnation Information Feature explains PVP part only."But those 30% are actually in effect everywhere as far as I tested, so consider either lack of information or an unexpected result of the feature by Devs"

Normal Attribute Power (Ruin , Spirit and Shadow )"So I guess this became like Pokemon now."(Ruin) >(Spirit)(Spirit) >(Shadow)(Shadow)>(Ruin)'>' Wins Over
Examples: When Spirit Power attacks Ruin Power, Spirit will deliver 30% less dmg to the Ruin Power Partners. But Ruin Power can hit Spirit Power with no % penalty + deal % based on reincarnation times First Reincarnation gives 16% damage.

Advanced Attribute Power (Soul , Destruction )
- These ones are the best Powers, only available with gold, they will reduce incoming damage from Opponents with Normal Attribute Power by 30%.
- When Soul attacking Destruction or Destruction attacking Soul, always reduces 30% of the damage on whoever attacks.(You noticed? A partner with Advanced Attributes will always reduce 30% from other Advanced or Normal Partners)
- Soul gives you X% final damage reduction (opponents do even less dmg), Destruction gives final damage bonus of X% (you deal more damage).
[Xis (10+(reincarnation times*6))%] Example {1st: 16%, 2nd: 22%, 3rd: 28%, 4th: 34%,...}

Beast Attribute Power
Referes to the 30% damage reduction given to all PvE enemies since this feature got implemented. It is simply saying that no attribute is strong against it, so it's not like there's one attribute that is specifically PvE based. Quoted from ~Kosmodestiny

Bonus Effects(Unlockable by upgrading reincarnation level, all Effects below have a % to happen)(Available on first reincarnation)
- Clear Shields "Kinda nice"
- 300% Damage to Enemy "Expect to 300% more when you deal skill or normal damage"
- Ignore Enemies Damage "This is like heaven for Vanguards or any other partner you want to ignore damage upon"
- Normal Attacks with All Team "This is useful unless your opponent his a Block master and you get high5's in the face, if you know what I mean.."

(Available on second reincarnation)
- When attacking ignore enemies defence "Very Nice stuff"
- When being attacked restore all HP"Very OP stuff" - Tested this, it heals you for your max HP when you attack, not when being attacked!
- Clear all enemy buffs "for OP people: Your prefered Hikifune counter, for the rest of people: you want more damage,defence,speed,critical,combo,HP regen? bananas,potatos,etc? You will get none!!!"

(Chances for triggering this better read the , will be based in how many times that partner been reincarnated)

Changing Bonus
To change bonus simply select the box's of what you want to change Attribute and/or Bonus,
the Advanced Attributes are also available for a certain chance but will cost 200gold/coupons to be able to do so!

Main Reincarnation
After you do a main reincarnation expect daily (Reincarnation Stone) rewards to boost your partners reincarnation faster. "Amount of 10 to start with after main reincarnates once, these are collectable everyday"
Expect hard times leveling your main up! Since you lack 30% Damage from this feature PVE (Evil Spirit mainly) will give less exp.To avoid exp loss on your partners try to reincarnate your partners first, before you reincarnate your main!

PS. This feature is all about trying to fix the insane 1 hit KO's and Starting Skills (that instantly wipes all opposition) making battles dull and easy, like this its possible to survive a bit

Good guide, I'm just going to help out a bit by correcting some of the features you weren't too sure on the details with.

Beast Attribute Power

Beast attribute power is not an attainable attribute power. It is referring to the 30% damage reduction given to all PvE enemies since this feature got implemented. It is simply saying that no attribute is strong against it, so it's not like there's one attribute that is specifically PvE based.

Bonus Effects (Appearently Not Implemented)

These bonus effects that you don't see available in the first reincarnation window slowly get unlocked as you increase in Reincarnation level. For example at R2 you will also be able to choose from the ignore defense, heal all hp, and clear target's buffs, as possible effects to be gained by your character. This essentially means that these "higher tier" effects are only attainable using soul refining stones since you will never be able to gain them as your random effect gained when you first hit R1.

After you do a main reincarnation expect daily Epic Exp Scroll rewards to boost your partners exp faster.

No scrolls are awarded atm. I'm not sure if this is a bug or they haven't implemented it yet, but you do get the 10 free reincarnation stones. I heard they should be giving out a new type of scroll (that has 1 million exp). Maybe because it's a new item, it hasn't been placed in yet?? I really don't know.